I'm a tech at a Sprint corporate store and whenever we have a customer in this situation and when the manual programming codes do not work we always suggest a hard reset of the device. This is the only way to get a Sprint iPhone back to the initial activation screen and will get everything back as far as data goes.
Worst case if that does not solve the issue we order the customer a replacement device at no charge if they have Sprints TEP program.
I wouldn't necessarily assume a device issue. It could simply be that the OP's area is undergoing Network Vision upgrades. If a tower is down for upgrades and there are no other close towers the iPhone may be fluctuating between roaming and a weak Sprint cell signal.
It'd be better to find out if the OP has this issue everywhere or just in one place I think. Yes, NV is mainly about LTE, but 3G is also undergoing upgrades and being connected to the fiber backhaul. And again, if a tower is down for upgrade…
OP, the code you keep inputting is not a magic bullet. All it is is a PRL update. A PRL update is simply a listing that your phone has that tells it in what priority to connect to towers. Sprint towers have higher priority, those with sharing agreements with Sprint less, and roaming towers (other carriers) even less. So, all you are doing essentially is downloading the same PRL update over and over again. It doesn't really solve anything.
There is indeed an issue with the kind of thing you are having. But I've heard that it's only iPhone 5 specific. As the tech mentioned, replacement is the only option for those phones because it's a fault in the hardware.
Lastly, as the tech suggested a restore - if you try that, before you turn your phone back on to run through the activation, let it sit off for a minimum of 30 minutes to allow the programming that Sprint uses to propigate to your device.
And, I just want to mention TEP. TEP is great, but dealing with Asurion is NOT. Applecare+ all the way. I am a Sprint customer and even though TEP was not available when I got my iPhone 5 I would not have gotten it anyway. I deal with Apple and not Sprint when it comes to service on my device. Apple replaced my iPhone 5 two months in, no questions asked and no dealing with TEP.